IMPROVED ACTION FUNCTIONALS IN NON-PERTURBATIVE QUANTUM GRAVITY

Models of gravity with variable G and Λ have acquired greater relevance after the recent evidence in favour of the Einstein theory being non-perturbatively renormalizable in the Weinberg sense. The present paper builds a modified Arnowitt–Deser–Misner (ADM) action functional for such models which leads to a power-law growth of the scale factor for pure gravity and for a massless ϕ⁴ theory in a Universe with Robertson–Walker symmetry, in agreement with the recently developed fixed-point cosmology. Interestingly, the renormalization-group flow at the fixed point is found to be compatible with a Lagrangian description of the running quantities G and Λ.